More on Scarf's Complementarity Problem and its Error Bounds
Article Type
Research Article
Publication Title
Asia Pacific Journal of Operational Research
Abstract
In this paper, we revisit Scarf's complementarity problem involving a rectangular matrix, known as the vertical block matrix introduced by [Cottle, RW and GB Dantzig (1970). A generalization of the linear complementarity problem. Journal of Combinatorial Theory, 8, 79-90]. We prove that the problem has a unique solution if the underlying matrix is a vertical block P-matrix. Some results on the error bounds for the vertical block P- and R0-matrices are derived. This further extends the results on global error bounds obtained by [Mathias, R and JS Pang (1990). Error bounds for the linear complementarity problem with a P-matrix. Linear Algebra and its Applications, 132, 123-136] and [Mangasarian, OL and J Ren (1994). New improved error bounds for the linear complementarity problem. Mathematical Programming, 66, 241-255].
DOI
10.1142/S0217595924500271
Publication Date
1-1-2024
Recommended Citation
Neogy, S. K.; Gupta, A.; and Mondal, P., "More on Scarf's Complementarity Problem and its Error Bounds" (2024). Journal Articles. 4911.
https://digitalcommons.isical.ac.in/journal-articles/4911